Hidden-Variable Theories  

In General > s.a. realism.
* Idea: Realist or Subquantum Theories; "Quantum mechanics is crazy; Nature is not crazy; So quantm mechanics is incomplete".
* Types: They an be deterministic or non-deterministic; There are currently (1995) three main approaches to quantum mechanics "without observers", in which observers do not play a central role, Bohm's approach (pilot-wave interpretation), Hartle's approach (consistent histories), and the Ghirardi-Rimini-Weber approach; Different types of "beable theories" are the de Broglie, Bohm, Bell, Vink, and modal interpretations.
* No-go theorems: There are results showing that hidden-variable theories, subject to appropriate hypotheses, cannot reproduce the predictions of quantum theory; For example, one cannot assign simultaneous unique values to all observables for a quantum system, unless they are contextual or the state space is 2D—or one generalizes the Kolmogorov probability axioms; 2016 (Cabello et al) Thermodynamic constraints.
* And probabilities: If the quantum mechanical description of reality is not complete and a hidden variable theory is possible, the question that arises is that of explaining where the rates of outcomes of statistical experiments come from, as pointed out by Landé and Popper; Answers have been proposed by Galvan and by Van Wesep; If we use non-Kolmogorovian probability axioms, we must accept the existence of finite null covers for some quantum mechanical experiments.
@ Reviews: Genovese PRP(05)qp/07; Hermens MS-a1002; Mermin & Schack FP(18)-a1805.
@ General: Bohm PR(52), PR(53); Kershaw PR(64); Bell RMP(66), in(71); Belinfante 73; Scully PRD(83); Mermin PRL(90); Fivel PRL(91); Dewdney JPA(92) [and pilot-wave theory, instructive]; Combourieu & Vigier PLA(93); Lanz IJTP(94); Bohm FP(96); Finkelstein PLA(96)qp/95 [measurement of beables]; Suppes et al NC-qp/96; Roy Pra(98)qp; Aerts IJTP(99)qp/01, qp/01-in; Lewis BJPS(06) [conspiracy theories]; Khrennikov NCB(06); Brandenburger & Yanofsky JPA(08)-a0711 [classification of properties]; Lokajíček a0905 [arguments in favor]; Abramsky SL(13)-a1007 [relational framework]; Brandenburger & Keisler a1401 [canonical hidden-variable space]; Weingarten a1709, a1802 [from many worlds, quantum complexity]; 't Hooft a2103-in [up to any desired accuracy].
@ No-go theorems: & Jauch & Piron, refutation Bohm & Bub RMP(66); Fine & Teller FP(78); Jordan & Sudarshan AJP(91)aug, comment Mermin AJP(91)jan; Methot CJP(06)qp/05-proc [rev]; Whitaker FP(07) [criticism of 1933 argument by Solomon]; Nagata FP-a0801 [unconditional]; Colbeck & Renner PRL(08)-a0801 [no non-trivial local parts], counter-arguments Wechsler a0907, Larsson & Cabello a0907, clarification a0907; Colbeck & Renner nComm(11)-a1005 [quantum theory cannot be extended]; Schlosshauer & Fine PRL(14); Chen et al a1507; Blass & Gurevich PRA(18)-a1509; Cuffaro BJPS(17)-a1509; Cabello et al PRA(16) [thermodynamic constraints]; Steeger & Teh a1712 [re rational incoherence and Dutch Book arguments].
@ On von Neumann's proof: Rosinger qp/04, TMP(05) [criticism]; Bub FP(10)-a1006 [reappraisal]; Bernstein a1102; Unnikrishnan a2105; > s.a. bell's inequality.
@ Types: Schneeloch et al a1603-wd [single Local Hidden Variable models]; Navarrete & Davis a1609 [fragile systems].
@ And probabilities: Galvan qp/04; Van Wesep AP(06)qp/05 [all phenomenological features of quantum observation are derivable from the hidden-variables premise]; Feintzeig & Fletcher FP(17)-a1608 [non-contextual, non-Kolmogorovian theories].

Related Topics > s.a. Fine's Theorem; history of quantum theory; pilot-wave interpretation; Retrocausation.
@ And Lorentz invariance: Squires PLA(90) [proposal]; Hardy PRL(92); Vaidman PRL(93); Hardy & Squires PLA(92); Horton & Dewdney JPA(01) [non-local, Lorentz-invariant]; Gisin PRA(11)-a1002 [no covariant non-local "hidden" variables]; Carmi et al a1903 [backwards in time signals]; > s.a. quantum field theory.
@ And locality / causality: Teufel et al PRA(97)qp/96; Watson PE(00)qp/02; Scarani & Gisin PLA(02) [superluminal signaling]; Valentini PLA(02)qp/01, in(02)qp/01 [instantaneous signals]; De Baere FP(05); Norsen FPL(06)qp [Bell locality]; Conway & Kochen FP(06) [not possible]; Boozer EJP(09) [two spin-1/2 particles]; Blood a1005 [locality and relativity of simultaneity]; Scarani et al FP(14) [superluminal signaling cannot remain hidden]; Hall a2009; > s.a. causality; locality.
@ Local theories: Pearle PRD(70) [two spin-1/2 particles], comment Gill Ent(20)-a1505; Marshall et al PLA(83) [and atomic cascade experiments]; Seipp FP(86) [stochastic]; Ferrero & Santos FP(97); Lewis FP(07); Matzkin a0706; Skotiniotis et al JMP(08)-a0707 [model for emulation of quantum mechanics]; Unnikrishnan a1102-conf; Oaknin a1411 [statistical model].
@ Non-local theories: Leggett FP(03) [incompatibility theorem]; Branciard et al PRL(07)-a0708 [inequalities and experimental falsification]; Branciard et al Nat(08)jul-a0801 [test of Leggett's proposal]; Pascazio a1012 [models incompatible with quantum mechanics]; Nikolić IJQI(12)-a1112 [solipsistic HVs], FP(12) [with non-locally related proper times]; Egg FP(13); van Enk a1506 [hidden quantum state]; Smolin a2105 [causal network]; > s.a. relativistic quantum mechanics.
@ Clauser-Horne correlation inequalities: Garg & Mermin PRL(82); Angelidis PRL(83), comment Garg & Leggett PRL(83), Barut & Meystre PRL(83), reply PRL(83) [criticism]; > s.a. CHSH Inequalities.
@ And spacetime structure: Valentini in(08)qp/05 [non-local signaling and simultaneity]; Tumulka BJPS(07)qp/06 [re values of observables].
@ Einstein's view: see issue FP(90)#8; Paty FP(95); Mehra 99; Holland FP(05)qp/04.
@ In favor: Thompson FPL(96)qp; Neumaier qp/99; 't Hooft qp/02-proc; Lokajíček NQ(10)-a1004 [Einstein-Bohr controversy].
@ Tests, specific systems: Clauser et al PRL(69); Fox & Rosner PRD(71); Panković PLA(89) [not possible]; Genovese PRA(04) [with neutral kaons]; Valentini ap/04 [black holes, Malus' law and entangled states]; Brida et al JPC(07)qp/06 [including stochastic electrodynamics]; Neumaier a0706 [single-photon experiment]; Santos a0706 [experiment that violates quantum predictions?]; Kyachko et al PRL(08) [for spin-1 systems]; Oliveira & Amarante-Segundo PhyA(09) [tunneling]; Hossenfelder FP(11)-a1105, JPCS(14)-a1401 [superdeterministic hidden variables, and test]; Oaknin a1805 [statistical model for the qutrit]; Gu et al a1808 [Bayesian analysis]; Li et al PRL(18)-a1808 [without detection and locality loopholes]; Chernega et al EPJD(19)-a1902 [for qubit states].
@ Related topics: Zisis FP(00) [approximate]; Valentini in(01)qp [early universe and statistical equilibrium]; Kalev et al FP(07)qp/06 [and entanglement]; Diósi a0708 [Grassmann variables]; Brunet a1210 [dynamical model and its failure]; Peil FP(12) [relative phase as hidden variable]; > s.a. quantum field theory.
@ Variations, generalizations: Loubenets JMP(15)-a1402 [quasi-hidden-variable models]; Arora et al a1607 [non-contextual hidden variable model]; Sen & Valentini a2003 [superdeterministic hidden-variable models].

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